fix(backend): correct "next weekday" and harden resolvers against model output

Four defects found by review of the preceding commits.

"next <weekday>" was occurrence-anchored ("this" plus seven) rather than week-
anchored. Said on a Thursday, "Thursday next week" resolved to +14 instead of
+7: next week runs Sat 10-18 to Fri 10-24, so its Thursday is 10-23, not 10-30.
A lab case a week late. "next" now counts from the start of the following
Saturday-start week, which also lets "this" and "next" correctly coincide —
said on a Thursday, "the coming Saturday" and "Saturday next week" are the same
day. "this" stays occurrence-anchored so it can never resolve into the past.

The other three all come from the same root cause: exported functions that are
reachable from untrusted model output must degrade, not throw or drop.

- a non-object `due` (the model emitting a bare string) was treated as "no
  deadline spoken" and silently discarded; only null/undefined mean absent now,
  anything else is flagged so the clinician sees something was heard and lost
- isJalaliLeapYear / jalaliDaysInMonth threw for years outside the conversion
  table, contradicting the module's own "degrade to null" contract; they now
  return false / 0, which also makes isValidJalaliDate's day check naturally
  false
- civilDateInZone passed a client-supplied zone straight to Intl, which raises
  RangeError before any fallback; it now validates and backstops to UTC, so a
  bad zone costs at most a day rather than a 500

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>

backend/src/common/zoned-civil-time.spec.ts

@@ -54,6 +54,14 @@ describe('zoned civil time', () => {
       expect(civilDateInZone(instant, 'Europe/Amsterdam')).toBe('2025-10-11');
     });
 
+    it('falls back to UTC on an invalid zone rather than throwing', () => {
+      // Intl raises RangeError on an unknown zone and this takes a client-supplied string.
+      const instant = new Date('2025-10-11T21:30:00.000Z');
+      expect(() => civilDateInZone(instant, 'Not/AZone')).not.toThrow();
+      expect(civilDateInZone(instant, 'Not/AZone')).toBe('2025-10-11');
+      expect(civilDateInZone(instant, '')).toBe('2025-10-11');
+    });
+
     it('zero-pads single-digit months and days', () => {
       expect(civilDateInZone(new Date('2025-01-05T12:00:00.000Z'), 'UTC')).toBe(
         '2025-01-05',